The present invention relates to the field of finite element simulation of extrusion processes.
It is to be understood that, although the description to follow mainly refers to aluminum as the extrusion material the principles of the present invention are equally applicable to other fields of extrusion, like polymer extrusion.
In the field of extrusion processes, algebraic equations are necessary to allow calculation of shapes of extrusion profiles. Chapters 1, 2 and 3 of B. J. E. van Rens, xe2x80x9cFinite element simulation of the aluminum extrusion processxe2x80x9d, thesis, Technical University Eindhoven, 1999, present systems of equations, for instance, those resulting from the conservation laws for mass, momentum and energy.
To arrive at these systems of algebraic equations, it is crucial that spatial discretizations of the relevant domains are available. However, the generation of these discretizations, from now on referred to as meshes, poses an enormous challenge due to the complex shapes that are associated with (aluminum) extrusion. As a result, existing meshing methods of the prior art either fail or generate an unacceptably large number of elements for these complex domains. Therefore, new, dedicated meshing algorithms have been presented by the inventor Van Rens in his thesis referred to above that generate meshes with which the solution field can be captured accurately while the number of elements is kept to a minimum. To make these dedicated algorithms as robust and flexible as possible they are restricted to the generation of triangular surface and tetrahedral volume elements.
Chapter 4 of Van Rens discloses algorithms that can be used by a computer system to generate meshes for the entire system of extrusion product and extrusion tool. In chapter 4.1.1 it is suggested that data from a Computer Aided Design (CAD) package with which the die has been designed can be used as input data for the mesh generator. However, it is not disclosed how this can be accomplished.
The present invention elaborates on the principles as explained in chapter 4 of the thesis of Van Rens, referred to above. The object of the invention is to provide a method and an arrangement for fully automatic mesh generation of the domains associated with the extrusion tools and the extrusion material in an extrusion process when the contours describing the cross-sections of the extrusion tools and the extrusion material are defined.
To that end, the present invention is directed to a computer arrangement for generating a mesh structure for an object, the object having an object volume enclosed by a front surface, a rear surface and an envelop surface, the front surface having a front surface cross-section and the rear surface having a rear surface cross-section substantially identical to the front surface cross-section, the computer arrangement being arranged for:
(a) receiving input data regarding a set of line sections together defining the front surface cross-section;
(b) defining a circle with a radius Lcirc, said radius Lcirc being just large enough to enclose an outer contour of the front surface cross-section;
(c) dividing each of the line sections into a number of consecutive line elements connected by nodes in accordance with the following equation:                                           n            el                    ⁡                      (            n            )                          =                              (                                          c                1                            ·                                                                    L                    sect                                    ⁡                                      (                    n                    )                                                                    L                  circ                                                      )                                c            2                                              (        1        )            
where:
nel(n)=number of line elements of line section 25(n)(n=1, 2, . . . , N)
Lsect(n)=length of line section 25(n)
c1=a first predetermined constant
c2=a second predetermined constant
(d) generating a front surface mesh using the line elements and nodes generated in step (c);
(e) copying the front surface mesh to the rear surface to generate a rear surface mesh;
(f) generating an envelop surface mesh for the envelop surface such that the envelop surface mesh is conform with the front surface mesh and with the rear surface mesh;
(g) generating a volume mesh for the object volume such that the volume mesh is conform with the front surface mesh, the rear surface mesh and the envelop surface mesh.
In another embodiment, the invention relates to meshing of a plurality of objects. Then the invention relates to a computer arrangement for generating a mesh structure for a plurality of objects including at least a first and a last object, each object having an object volume defined by a front surface, a rear surface and an envelop surface, the front surface having a front surface cross-section and the rear surface having a rear surface cross-section substantially identical to the front surface cross-section, the computer arrangement being arranged for:
(a) receiving input data regarding a set of line sections together defining the front surface cross-section of the first object;
(b) defining a circle with a radius Lcirc, said radius Lcirc being just large enough to enclose an outer contour of the front surface cross-section of the first object;
(c) dividing each of the line sections into a number of consecutive line elements connected by nodes in accordance with the following equation:                                           n            el                    ⁡                      (            n            )                          =                              (                                          c                1                            ·                                                                    L                    sect                                    ⁡                                      (                    n                    )                                                                    L                  circ                                                      )                                c            2                                              (        1        )            
where:
nel(n)=number of line elements of line section 25(n) (n=1, 2, . . . , N)
Lsect(n)=length of line section 25(n)
cel=a first predetermined constant
c2=a second predetermined constant
(d) generating front surface meshes for the first object using the line elements and nodes generated in step (c);
(e) copying front surface meshes of the first object to the rear surface of the first object to generate a rear surface mesh;
(f) generating an envelop surface mesh for the envelop surface of the first object such that the envelop surface mesh is conform with the front surface mesh and with the rear surface mesh of the first object;
(g) generating a volume mesh for the object volume of the first object such that the volume mesh is conform with the front surface mesh, the rear surface mesh and the envelop surface mesh of the first object;
(h) repeating steps (a) through (g) for those surfaces and volumes of all other objects not already meshed, such that meshes generated for volumes of different objects and located on interface surfaces between these volumes are conform.
In both these embodiments, automatically determining the line elements and nodes in this way may be done by the computer arrangement in a time frame of only minutes, whereas doing it manually may take hours, sometimes even weeks. In extrusion processes, the contours describing the cross-sections of the extrusion material inside and outside the extrusion tool may be manually input to the computer arrangement. This may took some hours. However, in a very advantageous embodiment, the input comprises line and curve segments from CAD data that defines the extrusion tool design. These data may be electronically available and, thus, electronically supplied to the computer arrangement, thus shortening the time to calculate meshes for extrusion arrangements significantly, e.g., to a few seconds.
The methods as referred to may advantageously be used when simulating with the computer arrangement physical behavior of the object(s) using a finite element analysis.